EBS206B
LECTURER: MIGABO ME
EMBEDDED SYSTEMS
10/05/2023
P MAKHUBELE
221253418
PRACTICAL 2: WORD PROBLEM
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TABLE OF CONTENTS
1. Description/intro………………………………………………………………………………….……………….3
2. Purpose/Aim………………………………………………………………………………………….………………3
3. Experimental design
3.1 Experimental Equipment…………………………………………………………………………………3
3.2 Parts List…………………………………………………………………………………………………………..3
3.3 Methology……………………………………………………………………………………………………….4
(a) Truth table
(b) K-Map
(c) Simplification
(d) Logic Circuit…………………………………………………………………………………………………5
4. Results/Findings………………………………………………………………………………………………………5
5. Comments and Conclusion……………………………………………………………………………………..6
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1.
Description/intro
Logic gates serve as the fundamental building blocks for constructing complex
circuits that power our modern technology. They operate based on the principles of
Boolean logic, allow us to process and manipulate information using binary signals of
1 and 0.
In this word problem, we delve into a captivating scenario that involves the
application of logic gates to solve a perplexing puzzle. By employing critical thinking
and logical reasoning, we aim to unravel the mystery behind a sequence of logic
gates and determine their combined output.
Our journey will challenge us to employ our understanding of logic gates, truth
tables, and the interactions between different gate types. As we navigate through
the problem, we will witness the remarkable power of these elementary
components and their role in shaping the digital world around us.
2.
Purpose/Aim
The aim is to design a logic circuit that monitors 4 doors. The circuit makes an LED
glow when:
• When all the doors are open at the same time, irrespective of the condition of
Conditions of other doors.
• When door1 and door2 are closed at the same time, irrespective of the condition
of the other doors.
• When door 3 is open and door 4 is closed, irrespective of the condition of the other
doors.
Using NAND gates only.
3.
Experimental Design
3.1Experimental Equipment
➢
➢
➢
➢
➢
➢
Breadboard
Connecting wires
LED
NAND Gates
DC Power Supply
Digital Multimeter
3.2Parts List
Board Reference
NAND-GATE
NAND GATE
NAND GATE
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Type
2-IN
2-IN
2-IN
Package
74HCT00
74HCT00
74HCT10
3.3 METHODOLOGY
(a) TRUTH TABLE
A
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
B
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
C
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
D
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
(b) K-MAP
AB\CD
00
01
11
10
00
0
1
0
1
01
0
0
0
0
11
1
1
0
1
10
1
1
0
1
̅ )(𝐴 + 𝐵 + 𝐶)
X = (𝐴̅ + 𝐵̅ )(𝐶 + 𝐷
(c) SIMPLIFICATION
̅ )(𝐴 + 𝐵 + 𝐶)
X = (𝐴̅ + 𝐵̅ )(𝐶 + 𝐷
̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
̅ )(𝐴 + 𝐵 + 𝐶)
𝑋̅ = (𝐴̅ + 𝐵̅ )(𝐶 + 𝐷
̿̿̿̿̿̿̿̿̿̿
̅ + 𝐵̅ ). ̿̿̿̿̿̿̿̿̿̿
̅ ). ̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿
(𝐶 + 𝐷
𝑋 = (𝐴
(𝐴 + 𝐵 + 𝐶)
𝑋 = ̅̅̅̅̅
𝐴. 𝐵 ∗ ̅̅̅̅̅
𝐶̅ . 𝐷 ∗ ̅̅̅̅̅̅̅̅̅̅̅̅
𝐴̅ ∗ 𝐵̅ ∗ 𝐶̅
̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿
̅̅̅̅̅
𝑋̿ = 𝐴.
𝐵 ∗ ̅̅̅̅̅
𝐶̅ . 𝐷 ∗ ̅̅̅̅̅̅̅̅
𝐴̅. 𝐵̅ . 𝐶̅
̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿
̅̅̅̅̅
𝑋 = 𝐴.
𝐵 ∗ ̅̅̅̅̅
𝐶̅ . 𝐷 ∗ ̅̅̅̅̅̅̅̅
𝐴̅. 𝐵̅ . 𝐶̅
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X
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
(d) LOGIC CIRCUIT
4. Results/Findings
In the built logic circuit above, an LED glow when:
• When all doors are open at the same time
• When door1 and door2 are close at the same time, irrespective of the
condition of the other doors
• When door3 is open and door4 is closed, irrespective of the condition of the
other doors.
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5. COMMENTS and CONCLUSION
As we conclude our exploration of the logic gate problem, we have witnessed the
incredible power and versatility of these fundamental components. By applying our
understanding of Boolean logic and the functionality of NAND gates, we successfully
deciphered the word problem and determined the output of the circuit.
Through this experience, we have gained valuable insights into the importance of
logical thinking and problem-solving skills in the world of technology.
In conclusion, our journey through the logic gate problem has reinforced the critical
role of logical reasoning and the significance of elementary components such as logic
gates in powering the digital world around us.
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